Related papers: Enforcing essential boundary conditions on domains…
Domain discretization is an essential part of the solution procedure in numerical simulations. Meshless methods simplify the domain discretization to positioning of nodes in the interior and on the boundary of the domain. However, generally…
We present an approach for solving optimal Dirichlet boundary control problems of nonlinear optics by using deep learning. For computing high resolution approximations of the solution to the nonlinear wave model, we propose higher order…
The Immersed Boundary Method (IBM) is one of the popular one-fluid mixed Eulerian-Lagrangian methods to simulate motion of droplets. While the treatment of a moving complex boundary is an extremely time consuming and formidable task in a…
Computer-Aided Design is ubiquitous in todays world, as almost every manufactured object begins as a digital model across industries. At the same time, advances in 3D sensing have made point clouds a dominant form of raw 3D data. Recovering…
Deep learning techniques for point cloud data have demonstrated great potentials in solving classical problems in 3D computer vision such as 3D object classification and segmentation. Several recent 3D object classification methods have…
Object detection from 3D point clouds remains a challenging task, though recent studies pushed the envelope with the deep learning techniques. Owing to the severe spatial occlusion and inherent variance of point density with the distance to…
Domain Generalization (DG) has been recently explored to improve the generalizability of point cloud classification (PCC) models toward unseen domains. However, they often suffer from limited receptive fields or quadratic complexity due to…
3D point cloud is an important 3D representation for capturing real world 3D objects. However, real-scanned 3D point clouds are often incomplete, and it is important to recover complete point clouds for downstream applications. Most…
In this paper, we propose a simple yet effective method to represent point clouds as sets of samples drawn from a cloud-specific probability distribution. This interpretation matches intrinsic characteristics of point clouds: the number of…
In this paper, we evaluate the effectiveness of deep operator networks (DeepONets) in solving both forward and inverse problems of partial differential equations (PDEs) on unknown manifolds. By unknown manifolds, we identify the manifold by…
For most finite element simulations, boundary-conforming meshes have significant advantages in terms of accuracy or efficiency. This is particularly true for complex domains. However, with increased complexity of the domain, generating a…
Robotic manipulation systems benefit from complementary sensing modalities, where each provides unique environmental information. Point clouds capture detailed geometric structure, while RGB images provide rich semantic context. Current…
Deep neural networks are known to be vulnerable to adversarial examples which are carefully crafted instances to cause the models to make wrong predictions. While adversarial examples for 2D images and CNNs have been extensively studied,…
Point clouds have become an increasingly important representation for 3D medical imaging, offering a compact, surface-preserving alternative to traditional voxel or mesh-based approaches. Recent advances in deep learning have enabled rapid…
When modeling scientific and industrial problems, geometries are typically modeled by explicit boundary representations obtained from computer-aided design software. Unfitted (also known as embedded or immersed) finite element methods offer…
Existing point cloud modeling datasets primarily express the modeling precision by pose or trajectory precision rather than the point cloud modeling effect itself. Under this demand, we first independently construct a set of LiDAR system…
Point clouds-based Networks have achieved great attention in 3D object classification, segmentation and indoor scene semantic parsing. In terms of face recognition, 3D face recognition method which directly consume point clouds as input is…
In this paper, we present a novel framework to solve differential equations based on multilayer feedforward network. Previous works indicate that solvers based on neural network have low accuracy due to that the boundary conditions are not…
Learning-based point cloud registration methods can handle clean point clouds well, while it is still challenging to generalize to noisy, partial, and density-varying point clouds. To this end, we propose a novel point cloud registration…
Boundary integral methods for the solution of boundary value PDEs are an alternative to `interior' methods, such as finite difference and finite element methods. They are attractive on domains with corners, particularly when the solution…